Hello B.
In the configuration of the strategy, you also define a storage type search, which I would setup to first look at the pallet area if the quantity to pick is > the pallet size, then to complete with the detailed picking. Also, there are some parameters to update in the material master.
Plus you have a lot of little ticks everywhere 
to try to fine tune the configuration (this is to be tried) and in the last resort there is still the possibility to add your own rules via exit :
I will try to setup an example later if possible although it looks like the evening is going to be long ...
Alexandre